Non-equilibrium superconductivity in superconducting resonators

D. J. Goldie; S. Withington

doi:10.1088/0953-2048/26/1/015004

paper

Non-equilibrium superconductivity in superconducting resonators

arXiv:1208.0685 · doi:10.1088/0953-2048/26/1/015004

Abstract

We have calculated the non-equilibrium quasiparticle and phonon distributions $f (E)$ , $n (Ω)$ , where $E$ and $Ω$ are the quasiparticle and phonon energies respectively, generated by the photons of the probe signal of a low temperature superconducting resonator SR operating well-below its transition temperature $T_{c}$ as the absorbed probe power per unit volume $P_{ab s}$ was changed. The calculations give insight into a rate equation estimate which suggests that the quasiparticle distributions can be driven far from the thermal equilibrium value for typical readout powers. From $f (E)$ the driven quasiparticle number density $N_{q p}$ and lifetime $τ_{r}$ were calculated. Using $N_{q p}$ we defined an effective temperature $T_{N}^{*}$ to describe the driven $f (E)$ . The lifetime was compared to the distribution averaged thermal lifetime at $T_{N}^{*}$ and good agreement was found typically within a few percent. We used $f (E)$ to model a representative SR. The complex conductivity and hence the frequency dependence of the experimentally measured forward scattering parameter $S_{21}$ of the SR as a function of $P_{ab s}$ were found. The non-equilibrium $S_{21}$ cannot be accurately modeled by a thermal distribution at an elevated temperature $T_{21}^{*}$ having a higher quality-factor in all cases studied and for low $P_{ab s}$ $T_{21}^{*} \sim T_{N}^{*}$ . Using $τ_{r}$ and $N_{q p}$ we determined the achievable Noise Equivalent Power of the resonator used as a detector as a function of $P_{ab s}$ . Simpler expressions for $T_{N}^{*}$ as a function of $P_{ab s}$ were derived which give a very good account of $T_{N}^{*}$ and also $N_{q p}$ and $τ_{r}$ . We conclude that multiple photon absorption from the probe increases the quasiparticle number above the thermal background and ultimately limits the achievable NEP of the resonator.

10 pages 8 figures

Non-equilibrium superconductivity in superconducting resonators

Abstract

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